Simple pendulum on Black hole

SIMPLE PENDULUM ON A BLACK HOLE

INTRODUCTION

A Black Hole is an extremely dense object in space time. It is formed after a super nova explosion if the remnant mass is greater than 5 solar masses. With a mass greater than 5 solar masses, the object collapses under its own gravity leading to a birth of a Black Hole. Consider a simple pendulum at the event horizon of a Black Hole ready to swing. A pendulum is a weight suspended from a pivot so that it can swing freely. It has a bob [mass] suspended from a frictionless pivot via a string. The central position of the bob i.e. when the pendulum is at rest is called its Mean position. When the bob is made to swing on the application of external force, it oscillates back and forth about this mean position. The maximum distance traversed by the bob from the mean position is known as amplitude. The amplitude is measured in radians which is a unit of angle. The time taken by the pendulum to complete one full oscillation is called the Time Period. For small amplitude less than 1 radian, the time period is independent of amplitude of the pendulum. We intend to determine the time period of such a pendulum on Black Hole.

A simple pendulum

ASSUMPTIONS

1. The string has no tension or compression

2. The pendulum is indestructible in the event horizon before it approaches the singularity.

3. Cosmic dust resistance is negligible

4. Effect of Gravitational Time dilation is negligible

CALCULATION

The time period of a simple pendulum is given by,

T = 2π*√ (l/g) (Eqn. 1)

Where,

T – Time period [s]

l – Length of the pendulum [m]

g – Acceleration due to gravity on Black Hole [m/s²]

g = ∞ m/s² (Eqn. 2)     

Let the length of pendulum be

l = 1 m (Eqn. 3)

Now substitute equations (2), (3) in equation (1)

T = 2π*√ (1/∞)

T = 2π*√ (0)

T = 2π*0

T = 0 s (Eqn. 4)                      

This is the time period of a simple pendulum on Black Hole. The value ‘zero’ clearly proves that time does not exist or time freezes inside a Black Hole. Assuming the pendulum is indestructible, it will not oscillate and just remain stationary about its mean position. No external force however large can oscillate the pendulum because time does not exist in the first place.

CONCLUSION

We thus determined the time period of a simple pendulum on Black Hole and concluded that the pendulum will never move since time does not exist inside a Black Hole.